Scalar mesons and the fragmented glueball

TL;DR

This paper tests the center-of-gravity rule for mesons, suggesting specific scalar mesons are spin-partners, and discusses the scalar glueball's role within meson wave functions, challenging the idea of it being an intruder.

Contribution

It provides a detailed analysis of scalar mesons' classification, mixing angles, and the role of the scalar glueball, proposing a consistent framework for understanding light scalar mesons.

Findings

Center-of-gravity rule holds well for heavy mesons.

Identifies scalar meson spin-partners and mixing angles.

Argues scalar glueball is part of meson wave functions, not an intruder.

Abstract

The center-of-gravity rule is tested for heavy and light-quark mesons. In the heavy-meson sector, the rule is excellently satisfied. In the light-quark sector, the rule suggests that the $a_0(980)$ could be the spin-partner of $a_2(1320)$, $a_1(1260)$, and $b_1(1235)$; $f_0(500)$ the spin-partner of $f_2(1270)$, $f_1(1285)$, and $h_1(1170)$; and $f_0(980)$ the spin-partner of $f_2'(1525)$, $f_1(1420)$, and $h_1(1415)$. From the decay and the production of light scalar mesons we find a consistent mixing angle $\theta^{\rm s}=(14\pm4)^\circ$. We conclude that $f_0(980)$ is likely "octet-like" in SU(3) with a slightly larger $s\bar s$ content and $f_0(500)$ is SU(3) "singlet-like" with a larger $n\bar n$ component. The $a_0(1450)$, $K^*_0(1430)$, $f_0(1500)$ and $f_0(1370)$ are suggested as nonet of radial excitations. The scalar glueball is discussed as part of the wave function of scalar isoscalar mesons and not as additional "intruder". It seems not to cause supernumerosity.